MCV4U - Practice Mastery Test #1

Transcription

1 Name: Class: Date: ID: A MCVU - Practice Mastery Test # Multiple Choice Identify the choice that best completes the statement or answers the question.. Solve a + b = a b = 5 a. a= & b=- b. a=- & b= c. a= & b= d. a= & b=-. Factor completely: x 0x + 5 a. (x + 5)(x 5) b. (x 5)(x 5) c. (x 5)(x ) d. (x 5). If (x + 5) 9 = 0 then a. x = or x = - b. x = ± c. x = ± d. x = or x = -. The equation x 6x + 8 = 0 has a. no real roots b. one real root c. two distinct real roots 5. Which of the following arrow diagrams illustrate functions? # # a. neither b. # only c. # only d. both # and # 6. A function f has I/O diagram Which of the following diagrams correspond to f? a. c. b. d. 7. A function is defined by y =. Its domain is x a. {x x 0, x ò} c. {x x, x ò} b. {x x > 0, x ò} d. {x x, x ò}

2 Name: ID: A 8. The equation of the image of y = x after a translation of units down is a. y = x + b. y = x + c. y = x d. y = x 9. The slope of the tangent to the graph of y = x + at x=5 is a. 0 b. 76 c. d The function defined by y = x +... has range a. {y y,y R} c. {y y,y R} b. {y y,y R} d. {y y,y R} x(x ). Evaluate lim x (x ) a. 0 b. c. 6 d. does not exist x(x ). Evaluate lim x x(x ) a. 0 b. c. 6 d. does not exist x(x ). Evaluate lim x (x ) a. 0 b. c. 6 d. does not exist x(x ). Evaluate lim x (x ) a. 0 b. c. 6 d. does not exist 5. Which of the following limits do not exist? i) lim x ii) lim x iii) lim x x + x x a. i) only b. ii) only c. iii) only d. i) and iii) 6. Evaluate lim x 0 x x (x ) a. 0 b. -.5 c. 6 d. does not exist x + h x 7. The expression lim h 0 h is most likely to be... a. the derivative of a function c. slope of a secant b. the value of a derivative d. none of the above

3 Name: ID: A (x + h) x 8. The expression lim h 0 h is most likely to be... a. the derivative of a function c. slope of a secant b. the value of a derivative d. none of the above ( + h) 6 9. The expression lim h 0 h is most likely to be... a. the derivative of a function c. slope of a secant b. the value of a derivative d. none of the above 0. The expression x + h x h is most likely to be... a. the derivative of a function c. slope of a secant b. the value of a derivative d. none of the above. P, ˆ 5 5 is a point on the unit circle and is on the terminal arm of angle θ. Which of the following is true?. a. sin θ = 5 and tan θ = c. sin θ = 5 and tan θ = b. cos θ = 5 and tan θ = d. cos θ = 5 and tan θ = In the diagram, C is closest to a. 67 b. c. 7 d.. Complete the identity sin θ = a. cos θ b. cos θ c. cosθ d. cos θ. sin π ˆ is equal to... a. b. + c. d. +

4 Name: ID: A 5. π ˆ cot is equal to... a. + c. undefined b. d What is the next number in the sequence,,0.5,0.5,...? a. 0.5 b. 0 c d Evaluate 5 a. 5 b. 5 c. 5 d Evaluate 7 a. b. 9 c. 6 d Simplify a a. a 6 a. Assume a 0 b. a c. a d. a 0. Simplify a. a a ˆ. Assume a 0 b. a 9 6 c. a d. a 5

5 MCVU - Practice Mastery Test # Answer Section MULTIPLE CHOICE. ANS: A While it is reasonable to solve the system algebraically, probably the easiest thing to do is to just check each pair of values in both equations. () +(-) () - (-) = - = + = - = 5 We notice that and b=- satisfy both equations, so it is the solution.. ANS: D Arrange the tiles into a rectangle: So x 0x + 5 = (x 5). ANS: C If (x + 5) 9 = 0 then x = 0. x = x = ±

6 . ANS: C The discriminant = b ac = ( 6) ()(7) = 6 8 = 8 Since the discriminant is greater than 0, the equation has two distinct real roots 5. ANS: C For a function, each element on the left must be mapped onto one element on the right. The diagram on the left shows one element of the domain mapping onto different elements of the range. 6. ANS: C In the original function, the first operation is to add, and then multiply by, so the inverse must perform the opposite operations in the opposite order (think... putting your sock on and then your shoe - the first thing you must do to reverse the process is to remove the shoe and then remove the sock), so... To undo multiply by, we must divide by. To undo add, we must subtract or add, so the I/O diagram for the inverse function is: 7. ANS: B In the real numbers, x is defined only if the expression under the square root symbol is greater or equal to 0, so x 0. However, if x was equal to 0, we would get y = 0 = 0 which would be undefined, so x must be just greater than 0 8. ANS: C This is a vertical transformation, so it is applied after the base function (square root). To translate units down, we want to subtract from the old values of y, so we can draw an input/output diagram as follows. To get the equation, juts apply the operations in sequence to x.

7 9. ANS: A Type the equation into Y on the calculator, GRAPH (and make sure the window is appropriate), then push nd PRGM to select DRAW. Push 5 to select TANGENT(, then push 5 and the calculator will display X=5 on the bottom of the graph. Press ENTER, and it will draw the tangent line at x=5 and will display the equation (approximate) on the bottom of the screen. In this case the equation listed is y=0x+-7. Its slope (0) is the instantaneous rate of change of the function at x=5. 0. ANS: C The I/O diagram for the function is... We know the base function has y 0, so we can work forwards through the I/O diagram to make determine that y Alternatively, we could use the calculator to graph it.. ANS: A x(x ) lim x (x ) = lim x(x ) since x x = ()( ) = 0. ANS: B lim x x(x ) x(x ) = lim since x,0 x =

8 . ANS: C lim x x(x ) (x ) = lim x since x x = () = 6. ANS: D x(x ) lim x (x ) x = lim x x since x which does not exist 5. ANS: A As x +, x is greater than, so x will negative, so exist. x will be undefined, so lim x + x does not As x, x is less than, so x will positive, so lim x = 0 x x will be defined and will approach 0, so As x, from either side, x is less than, so x will positive,, so lim x x = x will be defined, and will approach 6. ANS: A lim x 0 = lim x 0 = (0) (0 ) = 0 x x (x ) x (x ) since x 0

9 7. ANS: A If f(x) = x, then the expression is of the form lim h 0 8. ANS: A If f(x) = x, then the expression is of the form lim h 0 9. ANS: B If f(x) = x, then the expression is of the form lim h 0 at x=. f(x + h) f(x) h f(x + h) f(x) h f( + h) f() h which is the derivative. which is the derivative. = f () which is the value of the derivative 0. ANS: C If f(x) = x, then the expression is of the form (x,f(x)) to (x+h, f(x+h)). f(x + h) f(x) h which is the slope of a secant connecting. ANS: D The x coordinate of the point is cos θ, so cos θ = 5. The y coordinate of the point is sin θ, so sin θ = 5 and tan θ = sinθ cos θ = 5 5 =. ANS: D Sin C = opp hyp (any trig ratio could be used) = 5 sin 5 ˆ û Since C is acute, it is approximately 5

10 . ANS: B We know that cos θ + sin θ = for all θ. If we rearrange it (by subtracting sin θ from both sides) we get cos θ = sin θ. Another method is to substitute = cos θ + sin θ into the given expression to get: sin θ = cos θ + sin ˆ θ sin θ = cos θ + sin θ sin θ = cos θ. ANS: A cdsa 5. ANS: A cdsa 6. ANS: A Each term is 0.5 times the previous term (check by dividing consecutive terms), so if we take 0.5 and multiply it by 0.5, we get ANS: D 5 Note that order of operations requires you to apply the exponent to the 5 BEFORE the negative is = 5 applied. 8. ANS: D 7 = 7 = ( ) = 8 ˆ We are using the fact that x a b ˆ = x ab to split up the power. An exponent of means that you take the rd root of the base. I.e., = 7 so 7 =. 6

11 9. ANS: C a 6 a To divide powers with the same base, subtract the exponents. The common denominator is ANS: A ˆ a ˆ ˆ Reduce. To take the power of a power, multiply the exponents. Reduce. 7